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11-1 Inventory Management
William J. Stevenson
Operations Management
8th edition
11-2 Inventory Management
CHAPTER11
Inventory Management
McGraw-Hill/IrwinOperations Management, Eighth Edition, by William J. StevensonCopyright © 2005 by The McGraw-Hill Companies, Inc. All rights
reserved.
11-3 Inventory Management
Independent Demand
A
B(4) C(2)
D(2) E(1) D(3) F(2)
Dependent Demand
Independent demand is uncertain. Dependent demand is certain.
Inventory: a stock or store of goods
11-4 Inventory Management
Types of InventoriesTypes of Inventories
Raw materials & purchased parts Partially completed goods called
work in progress Finished-goods inventories
(manufacturing firms) or merchandise (retail stores)
11-5 Inventory Management
Types of Inventories (Cont’d)Types of Inventories (Cont’d)
Replacement parts, tools, & supplies
Goods-in-transit to warehouses or customers
11-6 Inventory Management
Functions of InventoryFunctions of Inventory
To meet anticipated demand
To smooth production requirements
To decouple operations
To protect against stock-outs
11-7 Inventory Management
Functions of Inventory (Cont’d)Functions of Inventory (Cont’d)
To take advantage of order cycles
To help hedge against price increases
To permit operations
To take advantage of quantity discounts
11-8 Inventory Management
Objective of Inventory ControlObjective of Inventory Control
To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds
Level of customer service
Costs of ordering and carrying inventory
11-9 Inventory Management
Why Inventory Control?Why Inventory Control?
11-10 Inventory Management
Why Inventory Control?Why Inventory Control?
Inadequate inventory control can result in both:
-understocking
-overstocking
Two fundamental decisions:
timing (when to order)
size (how much to order)
11-11 Inventory Management
A system to keep track of inventory
A reliable forecast of demand
Knowledge of lead times
Reasonable estimates of Holding costs
Ordering costs
Shortage costs
A classification system
Effective Inventory ManagementEffective Inventory Management
11-12 Inventory Management
Inventory Counting SystemsInventory Counting Systems
Periodic SystemPhysical count of items made at periodic intervals. Order is placed for variable amount rder is placed for variable amount after fixed passage of time.after fixed passage of time.
Perpetual (Continuous)Continuous) Inventory System System that keeps track of removals from inventory continuously, thus monitoringcurrent levels of each item. Constant amount is ordered whenConstant amount is ordered wheninventory declines to predetermined inventory declines to predetermined levellevel
11-13 Inventory Management
Inventory Counting Systems (Cont’d)Inventory Counting Systems (Cont’d)
Two-Bin System - Two containers of inventory; reorder when the first is empty
Universal Bar Code - Bar code printed on a label that hasinformation about the item to which it is attached
0
214800 232087768
11-14 Inventory Management
Lead time: time interval between ordering and receiving the order
Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year
Ordering costs: costs of ordering and receiving inventory
Shortage costs: costs when demand exceeds supply
Key Inventory TermsKey Inventory Terms
11-15 Inventory Management
ABC Classification SystemABC Classification System
Classifying inventory according to some measure of importance and allocating control efforts accordingly.
AA - very important
BB - mod. important
CC - least important
Figure 11.1
Annual $ value of items
AA
BB
CC
High
Low
Few ManyNumber of Items
11-16 Inventory Management
ABC ClassificationABC Classification
A items 15-20% of items that account for 75-80% of
annual inventory value B items
30-40% of items that account for 15% of annual inventory value
C items 40-50% of items that account for 10-15% of
annual inventory value
11-17 Inventory Management
ABC ClassificationABC Classification
11-18 Inventory Management
ABC Classification SystemABC Classification System
Item no.
Annual demand
Unit cost ($)
Annual value ($)
Classification
8 1,000 4,000 4,000,000 A
5 3,900 700 2,730,000 A
3 1,900 500 950,000 B
6 1,000 915 915,000 B
1 2,500 330 825,000 B
4 1,500 100 150,000 C
12 400 300 120,000 C
11 500 200 100,000 C
9 8,000 10 80,000 C
2 1,000 70 70,000 C
7 200 210 42,000 C
10 9,000 2 18,000 C
11-19 Inventory Management
Cycle CountingCycle Counting
A physical count of items in inventory
Cycle counting management
How much accuracy is needed?
When should cycle counting be performed?
Who should do it?
11-20 Inventory Management
The Inventory CycleThe Inventory CycleFigure 11.2
Profile of Inventory Level Over Time
Quantityon hand
Q
Receive order
Placeorder
Receive order
Placeorder
Receive order
Lead time
Reorderpoint
Usage rate
Time
11-21 Inventory Management
The Inventory CycleThe Inventory Cycle
11-22 Inventory Management
Economic order quantity model
Economic production model
Quantity discount model
Economic Order Quantity ModelsEconomic Order Quantity Models
11-23 Inventory Management
Only one product is involved
Annual demand requirements known
Demand is even throughout the year
Lead time does not vary
Each order is received in a single delivery
There are no quantity discounts
Assumptions of EOQ ModelAssumptions of EOQ Model
11-24 Inventory Management
The Inventory CycleThe Inventory CycleFigure 11.2
Profile of Inventory Level Over Time
Quantityon hand
Q
Receive order
Placeorder
Receive order
Placeorder
Receive order
Lead time
Reorderpoint
Usage rate
Time
11-25 Inventory Management
Carrying CostCarrying Cost
Annual carrying cost is computed by multiplying the average amount of inventory on hand by the cost to carry one unit for one year.
Annual carrying cost =
where
Q = order quantity in units
H = annual holding cost per unit
HQ
2
11-26 Inventory Management
Carrying costCarrying cost
Order quantity (Q)
Ann
ual c
ost H
Q
2
Carrying costs are linearly related to order size
11-27 Inventory Management
Ordering costOrdering cost
Annual ordering cost will decrease as order size increases because the larger the order size, the fewer orders are needed.
Annual ordering cost =
where
D = demand, usually units per year
S = ordering cost
SQ
D
11-28 Inventory Management
Ordering costOrdering costA
nnua
l cos
t
SQ
D
Ordering costs are inversely and non-linearly related to order size
Order quantity (Q)
11-29 Inventory Management
Total CostTotal Cost
Annualcarryingcost
Annualorderingcost
Total cost = +
Q2H D
QSTC = +
11-30 Inventory Management
Cost Minimization GoalCost Minimization Goal
Order Quantity (Q)
The Total-Cost Curve is U-Shaped
Ordering Costs
QO
An
nu
al C
os
t
(optimal order quantity)
TCQ
HD
QS
2
Carrying Costs
11-31 Inventory Management
Deriving the EOQDeriving the EOQ
Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.
Q = 2DS
H =
2(Annual Demand)(Order or Setup Cost)
Annual Holding CostOPT
11-32 Inventory Management
Minimum Total CostMinimum Total Cost
The total cost curve reaches its minimum where the carrying and ordering costs are equal.
To determine the order size at a minimum total cost.
Q = 2DS
H =
2(Annual Demand)(Order or Setup Cost)
Annual Holding CostOPT
11-33 Inventory Management
Example 1Example 1
A tyre distributor expects to sell 9,600 tyres next year. Annual carrying cost is RM16 per tyre and ordering cost is RM75. The distributor operates 288 days per year.
a) What is the EOQ?
b) How many times per year does the store order?
c) What is the length of an order cycle?
d) What is the total annual cost if the EOQ is ordered?
11-34 Inventory Management
Example 1Example 1
D = 9,600 tyres per year
H = RM16 per unit per year
S = RM75
b) Number of orders per year:
c) Time between orders:
tyresH
DSQa 300
16
)75)(600,9(22)
timesQ
D32
300
600,9
daysworking
yearaofyeartyres
tyres
D
Q
928832
1
32
1
/600,9
300
11-35 Inventory Management
Example 2Example 2
Taiko Manufacturing assembles security monitors. It purchases 3,600 CRT a year at $65 each. Ordering costs are $31 and annual carrying costs are 20% of purchase price.
a) Compute EOQ
b) Total annual cost.
11-36 Inventory Management
Example 2Example 2
D = 3,600 CRT per yearS = $31H = 0.20($65) = $13
b) Total annual cost:
CRTH
DSQa 131
13
)31)(600,3(22)
704,1$
)31(131
600,3)13(
2
131
2
SQ
DH
Q
11-37 Inventory Management
Production done in batches or lots Capacity to produce a part exceeds the part’s
usage or demand rate Assumptions of EPQ are similar to EOQ
except orders are received incrementally during production
Normally applies to a firm which is both a producer and user
Economic Production Quantity (EPQ)Economic Production Quantity (EPQ)
11-38 Inventory Management
Only one item is involved Annual demand is known Usage rate is constant Usage occurs continually Production rate is constant Lead time does not vary No quantity discounts
Economic Production Quantity AssumptionsEconomic Production Quantity Assumptions
11-39 Inventory Management
Economic Production QuantityEconomic Production QuantityProduction and usage
Usage only
Production
and usage
Usage only
Production and usage
Usage only
Cumulative production
Amount on hand
Run size, Qo
Maximum inventory, Imax
Time
EOQ with incremental inventory replenishment
11-40 Inventory Management
Economic Run SizeEconomic Run Size
upp
QI
p
QtimeRun
u
QtimeCycle
up
p
H
DSQ
SQ
DH
ITC
max
maxmin
2
2
Imax = maximum inventory
H = annual carrying cost
D = demand per year
S = setup cost
p = production rate
u = usage rate
11-41 Inventory Management
Example 3Example 3
A toy manufacturer uses 48,000 rubber wheels per year. The firm makes its own wheels, which it can produce at a rate of 800 per day. The carrying cost is $1 per wheel a year. Setup cost is $45. The firm operates 240 days per year. Determine the:
a) Optimal run size
b) Minimum total annual cost for carrying and setup
c) Cycle time for the optimal run size
d) Run time
11-42 Inventory Management
Example 3Example 3D = 48,000 wheels per year
H = $1 per wheel per year
S = $45
p =800 wheels per day
u = 48,000 wheels per 240 days, or 200 wheels per day.
b) TCmin =
wheelsup
p
H
DSQa 400,2
200800
800
1
)45)(000,48(22)
800,1$)45($2400
48000)1($
2
1800
800,1
)200800(800
2400)(
2
max
max
TC
wheels
upp
QI
SQ
DH
I
11-43 Inventory Management
Example 3Example 3
days
dayperwheels
wheels
p
QtimeRund
days
dayperwheels
wheels
u
QtimeCyclec
3
800
2400)
12
200
2400)
A run of wheels will be made every 12 days
Each run requires 3 days to complete
11-44 Inventory Management
Quantity DiscountsQuantity Discounts
Quantity discounts are price reductions for large orders offered to customers to induce them to buy in large quantities. For example:
Order Quantity Price per box
1 to 44 $2.00
45 to 69 1.70
70 or more 1.40
11-45 Inventory Management
Total Costs with Purchasing CostTotal Costs with Purchasing Cost
Annualcarryingcost
PurchasingcostTC = +
Q2H D
QSTC = +
+Annualorderingcost
PD +
11-46 Inventory Management
Total Costs with PDTotal Costs with PD
Co
st
EOQ
TC with PD
TC without PD
PD
0 Quantity
Adding Purchasing costdoesn’t change EOQ
Figure 11.7
11-47 Inventory ManagementTotal Cost with Constant Carrying Total Cost with Constant Carrying Costs Costs
OC
EOQ Quantity
To
tal C
os
t
TCa
TCc
TCbDecreasing Price
CC a,b,c
Figure 11.9
11-48 Inventory Management
Quantity Discount: ExampleQuantity Discount: Example
QUANTITYQUANTITY PRICEPRICE
1 - 491 - 49 $1,400$1,400
50 - 8950 - 89 1,1001,100
90+90+ 900900
HH = = $15 $15
SS = = $190 per computer $190 per computer
DD = = 200 units200 units
11-49 Inventory Management
When to Reorder with EOQ OrderingWhen to Reorder with EOQ Ordering
Reorder Point - When the quantity on hand of an item drops to this amount, the item is reordered
Safety Stock - Stock that is held in excess of expected demand due to variable demand rate and/or lead time.
11-50 Inventory Management
Determinants of the Reorder PointDeterminants of the Reorder Point
The rate of demand The lead time Demand and/or lead time variability Stockout risk (safety stock)
11-51 Inventory Management
Reorder Point (ROP)Reorder Point (ROP)
ROP can be expressed in terms of quantity. For example, a firm should place an order a
component when the number of components left is 50 units.
ROP= d x LT
where, d = demand rate (units per day or week)
LT = lead time in days or weeks
11-52 Inventory Management
Reorder Point: ExampleReorder Point: Example
Demand = 10,000 yards/yearDemand = 10,000 yards/year
Store open 311 days/yearStore open 311 days/year
Daily demand = 10,000 / 311 = 32.154 Daily demand = 10,000 / 311 = 32.154 yards/dayyards/day
Lead time = LT = 10 daysLead time = LT = 10 days
R = dLT = (32.154)(10) = 321.54 yardsR = dLT = (32.154)(10) = 321.54 yards
11-53 Inventory Management
Safety StockSafety Stock
LT Time
Expected demandduring lead time
Maximum probable demandduring lead time
ROP
Qu
an
tity
Safety stock
Figure 11.12
Safety stock reduces risk ofstockout during lead time
11-54 Inventory Management
Orders are placed at fixed time intervals Order quantity for next interval? Suppliers might encourage fixed intervals May require only periodic checks of
inventory levels Risk of stockout
Fixed-Order-Interval ModelFixed-Order-Interval Model
11-55 Inventory Management
Tight control of inventory items Items from same supplier may yield savings
in: Ordering Packing Shipping costs
May be practical when inventories cannot be closely monitored
Fixed-Interval BenefitsFixed-Interval Benefits
11-56 Inventory Management
Requires a larger safety stock Increases carrying cost Costs of periodic reviews
Fixed-Interval DisadvantagesFixed-Interval Disadvantages
11-57 Inventory Management
Single period model: model for ordering of perishables and other items with limited useful lives
Shortage cost: generally the unrealized profits per unit
Excess cost: difference between purchase cost and salvage value of items left over at the end of a period
Single Period ModelSingle Period Model
11-58 Inventory Management
Continuous stocking levels
Identifies optimal stocking levels
Optimal stocking level balances unit shortage and excess cost
Discrete stocking levels
Service levels are discrete rather than continuous
Desired service level is equaled or exceeded
Single Period ModelSingle Period Model
11-59 Inventory Management
Too much inventory Tends to hide problems Easier to live with problems than to eliminate
them Costly to maintain
Wise strategy Reduce lot sizes Reduce safety stock
Operations StrategyOperations Strategy
